Simplify the following expression: $ k = \dfrac{9}{10z - 6} + \dfrac{8}{9} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{9}{10z - 6} \times \dfrac{9}{9} = \dfrac{81}{90z - 54} $ Multiply the second expression by $\dfrac{10z - 6}{10z - 6}$ $ \dfrac{8}{9} \times \dfrac{10z - 6}{10z - 6} = \dfrac{80z - 48}{90z - 54} $ Therefore $ k = \dfrac{81}{90z - 54} + \dfrac{80z - 48}{90z - 54} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{81 + 80z - 48}{90z - 54} $ $k = \dfrac{80z + 33}{90z - 54}$